Calculating the Expectation and Variance of the Present Value for a Random Profit Stream of Uncertain Duration

Thomas B. Astebro (1) , Yigal Gerchak (1)

1 Department of Management Sciences

We derive the mean and variance of the random discounted sum [[[sigma].sup.N].sub.n=1] [[theta].sup.n][X.sub.n], when N is uncertain, as are the [X.sub.n]'s. This quantity arises in applications involving random cash-flows over an uncertain number of years. One such application is R&D projects, where both the magnitude and duration of cash-flows are uncertain at the time of investment decision. Previous models have assumed cash-flow duration to be certain. We relax this assumption. We then specialize these results to geometric, mixed-geometric and Poisson distributions of the cash-flow duration.

Keywords: Calculating; Expectation; Variance; Present Value; Random Profit Stream; Uncertain Duration

Domains: Strategy and business policy

Thomas B. Astebro, Yigal Gerchak. Calculating the Expectation and Variance of the Present Value for a Random Profit Stream of Uncertain Duration. Engineering Economics, 2000, 45 (4), pp.339-349. ⟨10.1080/00137910008967557⟩. ⟨hal-00648005⟩